When using the "Activate on blueprint activation" rollout configuration, cq:lastRolledOut date of the livecopy is updated which makes the livecopy up to date - which is wrong - and make the next deep rollout inefficient
As the content is not updated before the rollout, nothing is rolledout, but the page is considered as synchronized by the live copy overview
The "Activate on blueprint activation" is a rollout configuration with no content update.
Hence when the blueprint page is published, a rollout is started and then the cq:lastRolledOut date will be modified on the live copy.
That's the reason why the live copy overview will consider it as "Live copy up to date" with the blueprint, which is working as designed